NCERT Class 9 Science Exploration Chapter 07 Work Energy and Simple Machines PDF Download

Chapter 7: Work, Energy, and Simple Machines

In earlier Chapters 4 and 6, you have learnt how forces change the motion of objects, and how kinematic equations and Newton's laws can be used to analyse motion. But when forces change with time or act in complicated ways, applying these laws directly can become difficult. Is there a simpler and more powerful way to understand such situations? In this chapter, you will explore the ideas of work, energy and power, which often allow us to analyse motion and interactions more easily. You will also learn about simple machines, which help us perform tasks with less effort and more convenience. These form the building blocks of many everyday machines. Energy, which is the capacity to do work, lies at the heart of all these ideas and of almost every activity in our daily life (Fig. 7.1).

[Figure 7.1: Energy required to carry out tasks comes from various sources, See in your textbook]

We often use the words work, energy, and power in everyday conversations. As we learnt in Chapter 1, these terms have a precise meaning in science. Let us first understand how to define work.

Think It Over

• What will be the magnitude of velocity of the child at the bottom of the blue slide?
• Will two children of different masses reach the bottom of the same slide with the same velocity?
• Which of the slides will result in the largest magnitude of velocity for the child at its bottom?

7.1 Work Done by a Constant Force

Let us begin by doing some thinking based on our experience of lifting objects to a height.

Consider a wheat bag of mass 5 kg kept on the floor (Fig. 7.2a). Gravitational force \( mg \) acts downwards on the bag, where \( m \) is the mass of the bag and \( g \) is the acceleration due to gravity. To lift the bag slowly to a height of 1 m, you must apply an upward force equal to \( mg \). The force applied by you acts upwards on the bag as the bag is displaced through a distance of 1 m in the direction of the force. In everyday language, you would say that you did some work.

If you lift 3 such bags one after the other to the same height (Fig. 7.2b), you would have done 3 times more work than to lift 1 bag. If the bag is lifted to the same height by a machine using some fuel, it will require 3 times more fuel to lift 3 bags.

Now, suppose you lift all the 3 bags together to the same height (Fig. 7.2c). You would need to apply a force 3 times larger than that required for a single bag. Since, you have done the same task as in Fig. 7.2b, the work done by you would be 3 times the work required to lift 1 bag. This shows that applying a larger force over the same distance allows you to proportionally do more work.

Next, consider lifting a single 5 kg bag of wheat but to a height of 3 m (Fig. 7.2d). You would have carried out 3 times more work as compared to the work required to lift the same bag by 1 m. Or if the same machine is used three times in succession to lift the bag by 1 m each time, it would require 3 times more fuel. Thus, applying the same force over a larger distance allows you to proportionally do more work.

The scientific definition of work done by a force is based on the above observations. The work done by a constant force acting on an object in bringing about a certain displacement can be defined as:

work done on an object by a constant force = force applied \( \times \) displacement in the direction of the force \( \quad (7.1) \)

In the example that we discussed, the displacement was in the vertical direction, however, Eq. (7.1) can be used even if the force and displacement, both are in a horizontal direction, or any other direction for that matter.

For example, consider an object upon which a constant force \( F \) is acting, and it undergoes a displacement \( s \) in the direction of force (Fig. 7.3). Then, the work done \( W \) by the force on the object is

\[ W = F \times s \quad (7.2) \]

[Figure 7.2: Lifting bags to a height, See in your textbook]

[Figure 7.3: Work done by a force while displacing an object in (a) horizontal direction, and (b) vertical direction, See in your textbook]

Note

While describing the work done, it is important to specify the force (or agency) doing the work and the object on which the work is done.

Teacher's Note

In equation \( W = F \times s \), both the force and displacement must be in the same direction. If you push an object horizontally and it moves horizontally, the full force contributes to the work. But if you push at an angle, only the part of the force pointing along the displacement counts. For now, focus on cases where force and displacement are in the same direction.

The SI unit of work done is joule which is represented by J. The SI unit of force is the newton (N) and the SI unit of displacement is the metre (m). Thus, using Eq. (7.2), 1 joule can be defined as

\[ 1 \text{ J} = 1 \text{ N} \times 1 \text{ m} \]

That is, 1 joule of work is done on an object when a constant force of 1 newton is applied to it and it is displaced by 1 metre in the direction of the force. Since \( 1 \text{ N} = 1 \text{ kg m s}^{-2} \), note that

\[ 1 \text{ J} = 1 \text{ kg m s}^{-2} \times 1 \text{ m} = 1 \text{ kg m}^2 \text{ s}^{-2} \]

In the graph shown in Fig. 7.4, the force on an object is plotted on the Y-axis against the displacement in the direction of force on the X-axis. In this case, the work done on the object by the force is equal to the area of the shaded rectangle in the graph which is

\[ 10 \text{ N} \times 1 \text{ m} = 10 \text{ J} \]

Even when the force is not constant, work done can still be calculated by finding the area under the force - displacement graph between the initial and the final positions.

[Figure 7.4: Force-displacement graph, See in your textbook]

7.1.1 When is work done equal to zero?

From the definition of work done (Eq. 7.2), you can see that if the force acting on an object is zero, i.e., \( F = 0 \), then no work is done on the object. The work done on an object is also zero if there is no displacement of the object, i.e., \( s = 0 \), regardless of the force being applied on it. For example, if you apply a force on an object, such as a rigid wall (Fig. 7.5), there is no displacement in the wall and you have done no work on the wall.

This may seem odd because you feel tired. To apply a force, the muscles in your body repeatedly expand and contract, and use up the internal energy of your body. Thus, you may feel tired even though, in a scientific sense, you have not done any work on the object.

Ready to Go Beyond

If a force acts in a direction perpendicular to the displacement of an object, the work done by that force is zero (Fig. 7.6) because there is no displacement in the direction of the force. For example, when a girl carries a box while walking, she applies an upward force to balance its weight, while the box moves horizontally. Since, the force and displacement are perpendicular to each other, no work is done by this force on the box. In higher grades, you will learn how to calculate the work done when force and displacement are at an angle to each other.

[Figure 7.5: Pushing a wall, See in your textbook]

[Figure 7.6: Carrying a box, See in your textbook]

Teacher's Note

Remember: work is zero in three cases. First, if no force is applied (\( F = 0 \)). Second, if there is no movement (\( s = 0 \)). Third, if the force is perpendicular to the direction of movement. When you push against a wall that does not budge, you feel tired because your muscles use energy, but scientifically you have done zero work on the wall.

7.1.2 Positive and negative work done

The work done by a force on an object can either be positive or negative depending upon the relative directions of the force and the displacement. When the displacement is in the same direction as the applied force, the work done by the force on the object is said to be positive. For example,

Key Points

• Work is defined as force multiplied by displacement in the direction of the force: \( W = F \times s \). It is measured in joules (J), where 1 joule equals 1 newton \( \times \) 1 metre.
• Work done is zero when either the force is zero, there is no displacement, or the force and displacement are perpendicular to each other.
• The work done by a force is positive when the force and displacement are in the same direction, and negative when they are opposite.

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